Extremely convenient as they are, vectors
have a limitation that many novice C++ programmers frequently stumble upon:
iterators and references to an element of an vector
are invalidated when a preceding element is erased or when the vector expands
and needs to migrate its internal storage to a wider memory region (i.e.
when the required size exceeds the vector's capacity). We say then that
vectors are unstable: by
contrast, stable containers are those for which references and iterators
to a given element remain valid as long as the element is not erased: examples
of stable containers within the C++ standard library are list
and the standard associative containers (set,
map, etc.).

Sometimes stability is too precious a feature to live without, but one particular
property of vectors, element
contiguity, makes it impossible to add stability to this container. So, provided
we sacrifice element contiguity, how much can a stable design approach the
behavior of vector (random
access iterators, amortized constant time end insertion/deletion, minimal
memory overhead, etc.)? The following image describes the layout of a possible
data structure upon which to base the design of a stable vector:

Each element is stored in its own separate node. All the nodes are referenced
from a contiguous array of pointers, but also every node contains an "up"
pointer referring back to the associated array cell. This up pointer is the
key element to implementing stability and random accessibility:

Iterators point to the nodes rather than to the pointer array. This ensures
stability, as it is only the pointer array that needs to be shifted or relocated
upon insertion or deletion. Random access operations can be implemented by
using the pointer array as a convenient intermediate zone. For instance,
if the iterator it holds a node pointer it.p and
we want to advance it by n positions, we simply do:

it.p=*(it.p->up+n);

That is, we go "up" to the pointer array, add n there and then
go "down" to the resulting node.

General properties. stable_vector
satisfies all the requirements of a container, a reversible container and
a sequence and provides all the optional operations present in vector. Like
vector, iterators are random access. stable_vector
does not provide element contiguity; in exchange for this absence, the container
is stable, i.e. references and iterators to an element of a stable_vector remain valid as long as the
element is not erased, and an iterator that has been assigned the return
value of end() always remain valid until the destruction of the associated
stable_vector.

Operation complexity. The big-O complexities
of stable_vector operations
match exactly those of vector. In general, insertion/deletion is constant
time at the end of the sequence and linear elsewhere. Unlike vector, stable_vector does not internally perform
any value_type destruction, copy/move construction/assignment operations
other than those exactly corresponding to the insertion of new elements or
deletion of stored elements, which can sometimes compensate in terms of performance
for the extra burden of doing more pointer manipulation and an additional
allocation per element.

Memory overhead. The C++ standard does not
specifiy requirements on memory consumption, but virtually any implementation
of vector has the same behavior
wih respect to memory usage: the memory allocated by a vector
v with n elements of type T is

mv = c∙e,

where c is v.capacity()
and e is sizeof(T). c can
be as low as n if the user has explicitly reserved the exact capacity required;
otherwise, the average value c for a growing vector
oscillates between 1.25∙n and 1.5∙n for typical resizing policies.
For stable_vector, the memory
usage is

msv = (c + 1)p + (n + 1)(e + p),

where p is the size of a pointer. We have c + 1 and n + 1 rather than c and
n because a dummy node is needed at the end of the sequence. If we call f
the capacity to size ratio c/n and assume that n is large enough, we have
that

msv/mv ≃ (fp + e + p)/fe.

So, stable_vector uses less
memory than vector only when
e > p and the capacity to size ratio exceeds a given threshold:

Summary. stable_vector
is a drop-in replacement for vector
providing stability of references and iterators, in exchange for missing
element contiguity and also some performance and memory overhead. When the
element objects are expensive to move around, the performance overhead can
turn into a net performance gain for stable_vector
if many middle insertions or deletions are performed or if resizing is very
frequent. Similarly, if the elements are large there are situations when
the memory used by stable_vector
can actually be less than required by vector.

“Red-black trees aren't the only way to organize data that
permits lookup in logarithmic time. One of the basic algorithms of computer
science is binary search, which works by successively dividing a range in
half. Binary search is log N and it doesn't require any fancy data structures,
just a sorted collection of elements. (...) You can use whatever data structure
is convenient, so long as it provides STL iterator; usually it's easiest
to use a C array, or a vector.”

“Both std::lower_bound and set::find take time proportional
to log N, but the constants of proportionality are very different. Using
g++ (...) it takes X seconds to perform a million lookups in a sorted vector<double>
of a million elements, and almost twice as long (...) using a set. Moreover,
the set uses almost three times as much memory (48 million bytes) as the
vector (16.8 million).”

“Using a sorted vector instead of a set gives you faster
lookup and much faster iteration, but at the cost of slower insertion. Insertion
into a set, using set::insert, is proportional to log N, but insertion into
a sorted vector, (...) , is proportional to N. Whenever you insert something
into a vector, vector::insert has to make room by shifting all of the elements
that follow it. On average, if you're equally likely to insert a new element
anywhere, you'll be shifting N/2 elements.”

“It may sometimes be convenient to bundle all of this together
into a small container adaptor. This class does not satisfy the requirements
of a Standard Associative Container, since the complexity of insert is O(N)
rather than O(log N), but otherwise it is almost a drop-in replacement for
set.”

Following Matt Austern's indications, Andrei Alexandrescu's Modern
C++ Design showed AssocVector,
a std::map drop-in replacement designed in his
Loki library:

“It seems as if we're better off with a sorted vector. The
disadvantages of a sorted vector are linear-time insertions and linear-time
deletions (...). In exchange, a vector offers about twice the lookup speed
and a much smaller working set (...). Loki saves the trouble of maintaining
a sorted vector by hand by defining an AssocVector class template. AssocVector
is a drop-in replacement for std::map (it supports the same set of member
functions), implemented on top of std::vector. AssocVector differs from a
map in the behavior of its erase functions (AssocVector::erase invalidates
all iterators into the object) and in the complexity guarantees of insert
and erase (linear as opposed to constant). ”

Boost.Containerflat_[multi]map/set containers are ordered-vector based
associative containers based on Austern's and Alexandrescu's guidelines.
These ordered vector containers have also benefited recently with the addition
of movesemantics
to C++, speeding up insertion and erasure times considerably. Flat associative
containers have the following attributes:

Faster lookup than standard associative containers

Much faster iteration than standard associative containers

Less memory consumption for small objects (and for big objects if shrink_to_fit is used)

Improved cache performance (data is stored in contiguous memory)

Non-stable iterators (iterators are invalidated when inserting and erasing
elements)

When the standard template library was designed, it contained a singly linked
list called slist. Unfortunately,
this container was not standardized and remained as an extension for many
standard library implementations until C++11 introduced forward_list,
which is a bit different from the the original SGI slist.
According to SGI STL
documentation:

“An slist
is a singly linked list: a list where each element is linked to the next
element, but not to the previous element. That is, it is a Sequence that
supports forward but not backward traversal, and (amortized) constant time
insertion and removal of elements. Slists, like lists, have the important
property that insertion and splicing do not invalidate iterators to list
elements, and that even removal invalidates only the iterators that point
to the elements that are removed. The ordering of iterators may be changed
(that is, slist<T>::iterator might have a different predecessor or
successor after a list operation than it did before), but the iterators themselves
will not be invalidated or made to point to different elements unless that
invalidation or mutation is explicit.”

“The main difference between slist
and list is that list's iterators are bidirectional iterators, while slist's
iterators are forward iterators. This means that slist
is less versatile than list; frequently, however, bidirectional iterators
are unnecessary. You should usually use slist
unless you actually need the extra functionality of list, because singly
linked lists are smaller and faster than double linked lists.”

“Important performance note: like every other Sequence,
slist defines the member
functions insert and erase. Using these member functions carelessly, however,
can result in disastrously slow programs. The problem is that insert's first
argument is an iterator pos, and that it inserts the new element(s) before
pos. This means that insert must find the iterator just before pos; this
is a constant-time operation for list, since list has bidirectional iterators,
but for slist it must find
that iterator by traversing the list from the beginning up to pos. In other
words: insert and erase are slow operations anywhere but near the beginning
of the slist.”

“Slist provides the member functions insert_after and erase_after,
which are constant time operations: you should always use insert_after and
erase_after whenever possible. If you find that insert_after and erase_after
aren't adequate for your needs, and that you often need to use insert and
erase in the middle of the list, then you should probably use list instead
of slist.”

Boost.Container updates the classic slist container with C++11 features like
move semantics and placement insertion and implements it a bit differently
than the standard C++ forward_list.
forward_list has no size()
method, so it's been designed to allow (or in practice, encourage) implementations
without tracking list size with every insertion/erasure, allowing constant-time
splice_after(iterator,forward_list&,iterator,iterator)-based
list merging. On the other hand slist
offers constant-time size() for those that don't care about linear-time
splice_after(iterator,slist&,iterator,iterator)size()
and offers an additional splice_after(iterator,slist&,iterator,iterator,size_type) method that can speed up slist
merging when the programmer already knows the size. slist
and forward_list are therefore
complementary.